20153330Solving high-order partial differential equations in unbounded domains by means of double exponential second kind Chebyshev approximation22In this paper, a collocation method for solving high-order linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of derivatives. All principles and properties of the ESC functions are derived and introduced by us as a new basis defined in the whole range. The method transforms the PDEs and conditions into block matrix equations, which correspond to system of linear algebraic equations with unknown ESC coefficients, by using ESC collocation points. Combining these matrix equations and then solving the system yield the ESC coefficients of the solution function. Numerical examples are included to test the validity and applicability of the method.1-147162--MohamedAbd ElsalamMathematics Department, Faculty of Science
Al-Azhar University, Nasr-City, 11884, Cairo, EgyptMathematics Department, Faculty of Science
Egyptmohamed_salam1985@yahoo.com--MohamedRamadanMathematics Department, Faculty of Science, Menoufia University, Shebein El-Koom, EgyptMathematics Department, Faculty of Science,Egyptramadanmohamed13@yahoo.com--KamalRaslsnMathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, EgyptMathematics Department, Faculty of Science,Egyptkamal_raslan@yahoo.com--TalaatEl DanafDepartment of Mathematics and Statistics, Taibah University Madinah Munawwarah, KSADepartment of Mathematics and Statistics,Saudi Arabiatalaat11@yahoo.comExponential second kind Chebyshev functionsHigh-order partial differential equationsCollocation methodITERATIVE SCHEME TO A COUPLED SYSTEM OF HIGHLY NONLINEAR FRACTIONAL ORDER DIFFERENTIAL EQUATIONS22In this article, we investigate sufficient conditions for existence of maximal and minimalsolutions to a coupled system of highly nonlinear differential equations of fractional order with mixedtype boundary conditions. To achieve this goal, we apply monotone iterative technique togetherwith the method of upper and lower solutions. Also an error estimation is given to check theaccuracy of the method. We provide an example to illustrate our main results.1-163176--KamalShahUniversity of MalakandUniversity of MalakandPakistankamalshah408@gmail.com--RahmatKhanDerartment of Mathematcs University of Malakand KPK PakistanDerartment of Mathematcs University of MalakandPakistanrahmat_alipk@yahoo.comCoupled systemMixed type boundary conditions, Upper and lower solutions, Monotone iterative technique, Existence and uniqueness resultsSolution of Bang-Bang Optimal Control Problems by Using Bezier Polynomials22In this paper, a new numerical method is presented for solving the optimal control problems of Bang-Bang type with free or fixed terminal time. The method is based on Bezier polynomials which are presented in any interval as $[t_0,t_f]$. The problems are reduced to a constrained problems which can be solved by using Lagrangian method. The constraints of these problems are terminal state and conditions. Illustrative examples are included to demonstrate the validity and applicability of the method.1-177191--AyatollahYariPayame Noor UniversityPayame Noor UniversityI. R. Irana_yary@yahoo.com--MirkamalMirniaUniversity of TabrizUniversity of TabrizI. R. Iranmirnia-kam@tabrizu.ac.ir--AghilehHeydariPayame Noor UniversityPayame Noor UniversityI. R. Irana_heidari@pnu.ac.irOptimal controlBang-Bang controlMinimum-timeBezier polynomials familyBest approximationExplicit exact solutions for variable coefficient Broer-Kaup equations22Based on symbolic manipulation program Maple and using Riccati equation mapping method several explicit exact solutions including kink, soliton-like, periodic and rational solutions are obtained for (2+1)-dimensional variable coefficient Broer-Kaup system in quite a straightforward manner. The known solutions of Riccati equation are used to construct new solutions for variable coefficient Broer-Kaup system.1-192199--ManjitSinghYadavindra College of Engineering, Punjabi University Guru Kashi Campus, Talwandi SaboYadavindra College of Engineering, PunjabiIndiamanjitcsir@gmail.com--R.K.GuptaCentral University of Punjab, Bathinda, Punjab, India.Central University of Punjab, Bathinda, Punjab,Indiarajeshgupt@thapar.eduBroer-Kaup equationsRiccati equation mapping methodExplicit exact solutionsAn application of differential transform method for solving nonlinear optimal control problems22In this paper, we present a capable algorithm for solving a class of nonlinear optimal control problems (OCP's). The approach rest mainly on the differential transform method (DTM) which is one of the approximate methods. The DTM is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. Utilizing this approach, the optimal control and the corresponding trajectory of the OCP's are found in the form of rapidly convergent series with easily computed components. Numerical results are also given for several test examples to demonstrate the applicability and the efficiency of the method.1-200217--AlirezaNazemiFaculty of math shahrood university.Faculty of math shahrood university.I. R. Irannazemi20042003@gmail.comOptimal Control ProblemsDifferential transform methodHamiltonian systemNon-polynomial Spline Method for Solving Coupled Burgers Equations22In this paper, non-polynomial spline method for solving Coupled Burgers Equations are presented. We take a new spline function. The stability analysis using Von-Neumann technique shows the scheme is unconditionally stable. To test accuracy the error norms 2L, L are computed and give two examples to illustrate the sufficiency of the method for solving such nonlinear partial differential equations. These results show that the technique introduced here is accurate and easy to apply.1-218230--KhalidK. Alidepartment of mathematics, faculty of since, al-azhar univesitydepartment of mathematics, faculty of since,Egyptkhalidkaram2012@yahoo.com--KamalRaslanMathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt.Mathematics Department, Faculty of Science,Egyptkamal_raslan@yahoo.com--TalaatEl DanafMathematics Department, Faculty of Science, Menoufia University, Shebein El-Koom, Egypt.Mathematics Department, Faculty of Science,Saudi Arabiatalaat11@yahoo.comNon-polynomialspline methodCoupledBurger’sEquations